Velocity factor

Short description: Ratio of the speed at which a wavefront passes through the medium to the speed of light in vacuum

The velocity factor (VF),[1] also called wave propagation speed or velocity of propagation (VoP or [math]\displaystyle{ v_\mathrm{P} }[/math]),[2] of a transmission medium is the ratio of the speed at which a wavefront (of an electromagnetic signal, a radio signal, a light pulse in an optical fibre or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.

The speed of radio signals in vacuum, for example, is the speed of light, and so the velocity factor of a radio wave in vacuum is 1.0 (unity). In electrical cables, the velocity factor mainly depends on the insulating material (see table below).

The use of the terms velocity of propagation and wave propagation speed to mean a ratio of speeds is confined to the computer networking and cable industries. In a general science and engineering context, these terms would be understood to mean a true speed or velocity in units of distance per time,[3] while velocity factor is used for the ratio.

## Contents

* 1 Typical velocity factors
* 2 Calculating velocity factor
* 2.1 Electric wave
* 2.2 Optical wave
* 3 See also
* 4 References

## Typical velocity factors

Velocity factor is an important characteristic of communication media such as category 5 cables and radio transmission lines. Plenum data cable typically has a VF between 0.42 and 0.72 (42% to 72% of the speed of light in vacuum) and riser cable around 0.70 (approximately 210,000,000 m/s or 4.76 ns per metre).

Minimum velocity factors for network cables  VF (%) | Cable | Ethernet physical layer

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74–79 | Cat-7 twisted pair |
77 | RG-8/U | Minimum for 10BASE5[4]
67 | Optical fiber (silica glass) | Minimum for 10BASE-FL,[5] 100BASE-FX, ...
67 | Plastic optical fiber (PMMA) | 1000BASE-RHx
63 | Plastic optical fiber (polystyrene)
65 | RG-58A/U | Minimum for 10BASE2[6]
65 | Cat-6A twisted pair | 10GBASE-T
64 | Cat-5e twisted pair | 100BASE-TX, 1000BASE-T
58.5 | Cat-3 twisted pair | Minimum for 10BASE-T[7]

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table:[8][9]

VF (%) | Transmission line

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95–99 | Open-wire "Ladder" Line
93 | HJ8-50B 3 inch Heliax coaxial cable (air dielectric)[10]
86 | RG-8 Belden 7810A coaxial cable (gas-injected foam high-density polyethylene)[11]
83 | RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
82 | RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
80 | Belden 9085 twin-lead
77 | RG-8/U generic (foamed polyethylene)
66 | Belden 8723 twin shielded twisted pair stranded (polypropylene insulator)[12]
66 | RG-213 CXP213 (solid polyethylene dielectric)

## Calculating velocity factor

### Electric wave

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), [math]\displaystyle{ \kappa }[/math] or [math]\displaystyle{ \epsilon_\mathrm{r} }[/math], of the material through which the signal passes:

[math]\displaystyle{ \mathrm{VF} = { \frac{1}{\sqrt{\kappa}} } \ }[/math]

in the usual case where the relative permeability, [math]\displaystyle{ \mu_\mathrm{r} }[/math], is 1. In the most general case:

[math]\displaystyle{ \mathrm{VF} = { \frac{1}{\sqrt{\mu_\mathrm{r}\epsilon_\mathrm{r}}} } \ }[/math]

which includes unusual magnetic conducting materials, such as ferrite.

The velocity factor for a lossless transmission line is given by:

[math]\displaystyle{ \mathrm{VF} = { \frac{1}{c_\mathrm{0}\sqrt{L'C'}} } \ }[/math]

where [math]\displaystyle{ L' }[/math] is the distributed inductance (in henries per unit length), [math]\displaystyle{ C' }[/math] is the capacitance between the two conductors (in farads per unit length), and [math]\displaystyle{ c_\mathrm{0} }[/math] is the speed of light in vacuum.

### Optical wave

VF equals the reciprocal of the refractive index [math]\displaystyle{ {n} }[/math] of the medium, usually optical fiber.

[math]\displaystyle{ \mathrm{VF} = { \frac{1}{n} } \ }[/math]

## See also

* Coaxial cable
* Propagation delay
* Signal velocity
* Speed of electricity
* Speed of sound
* Telegrapher's equations

## References

1. ↑ Gottlieb, I.M., Practical RF power design techniques, TAB Books, 1993, ISBN:0-8306-4129-7, p.251 ('velocity factor')
2. ↑ Velocity of Propagation, General Cable Australia Pty Ltd, retrieved 2010-02-13
3. ↑ "velocity of propagation" in Walker, P.M.B., Chambers Science and Technology Dictionary, Edinburgh, 1991, ISBN:1-85296-150-3
4. ↑ IEEE 802.3 Clause 8.4.1.3
5. ↑ IEEE 802.3 Clause 15.3.1.3
6. ↑ IEEE 802.3 Clause 10.5.1.3
7. ↑ IEEE 802.3 Clause 14.4.2.4
8. ↑ H. Ward Silver, ed (2011). "Chapter 22: Component Data and References". The ARRL Handbook For Radio Communications (88th ed.). ARRL. p. 22.48. ISBN 978-0-87259-096-0.
9. ↑ Kaiser, Kenneth L. (2005). Transmission Lines, Matching, and Crosstalk. CRC Press. pp. 2–24. ISBN 978-0-8493-6362-7. https://books.google.com/books?id=QWFd-33xXvgC&pg=SA2-PA24.
10. ↑ "HJ8-50B". https://www.commscope.com/globalassets/digizuite/112335-p360-hj8-50b-external.pdf?r=1.
11. ↑ "Belden Global Catalog". https://catalog.belden.com/techdata/EN/7810A_techdata.pd.
12. ↑ "8723 Multi-Conductor - Shielded Twisted Pair Cable". http://www.belden.com/techdatas/english/8723.pdf.

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